Here is my rather simple idea. I will treat the set of real numbers as a set of discrete continuities, each separated by an Epsilon ball that tends to 0.

So, let's say P(b) is true. We then assume P(k) is true, and prove that P(k+e) is true, where e goes to zero.

I just want to know if this is a valid technique or not because our teacher said that mathematical induction can only be applied to discrete structures, but I see no difficulty in treating a continuous system as a set of infinitesimal discrete quantities. Mak